CN113466924B - Symmetrical warhead pulse forming device and method - Google Patents
Symmetrical warhead pulse forming device and method Download PDFInfo
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- CN113466924B CN113466924B CN202110746562.0A CN202110746562A CN113466924B CN 113466924 B CN113466924 B CN 113466924B CN 202110746562 A CN202110746562 A CN 202110746562A CN 113466924 B CN113466924 B CN 113466924B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01T—MEASUREMENT OF NUCLEAR OR X-RADIATION
- G01T1/00—Measuring X-radiation, gamma radiation, corpuscular radiation, or cosmic radiation
- G01T1/36—Measuring spectral distribution of X-rays or of nuclear radiation spectrometry
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Abstract
The invention discloses a symmetrical warhead pulse forming device and a symmetrical warhead pulse forming method, which are characterized in that a nuclear radiation signal acquisition module is used for acquiring a nuclear radiation signal and processing the nuclear radiation signal into discrete negative index nuclear pulses x (n); and then processing the discrete negative index nuclear pulse x (n) through a digital nuclear signal processing module to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to a terminal for display. The symmetrical warhead pulse forming device provided by the invention has the advantages of simple structure, small operand and convenience for implementation in an FPGA; meanwhile, the symmetrical warhead pulse forming method provided by the invention meets the technical requirements of energy resolution, pulse passing rate and the like, and has adjustable pulse forming parameters and strong self-adaptability.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a symmetrical warhead pulse forming device and method.
Background
With the rapid development of scientific technology, the traditional analog multichannel technology has been unable to meet the current nuclear radiation measurement demand due to the defects of complex circuit structure, high design cost, large power consumption, large influence of environmental factors on analog devices and the like, and the high-performance digital multichannel technology is becoming the mainstream gradually. The digital nuclear pulse forming technology is key to digital multichannel technology, and a simple and high-performance digital nuclear pulse forming algorithm can not only reduce the influence of electronic noise, ballistic deficit, pulse accumulation and the like on energy and time resolution, but also give consideration to energy resolution and pulse passing rate, and improve the flexibility and the self-adaptability of a system.
Disclosure of Invention
The invention aims to overcome the defects of the existing analog multichannel technology, and provides a symmetrical warhead pulse forming device and method, which adopt a digital symmetrical warhead pulse forming mode to improve the energy resolution, anti-accumulation and ballistic defect of energy spectrum measurement.
The technical scheme of the invention is as follows: the symmetrical warhead pulse forming device comprises a nuclear radiation signal acquisition module and a digital nuclear signal processing module, wherein the output end of the nuclear radiation signal acquisition module is connected with the input end of the digital nuclear signal processing module, and the output end of the digital nuclear signal processing module is connected with a terminal; the nuclear radiation signal acquisition module is used for acquiring nuclear radiation signals and processing the nuclear radiation signals into discrete negative index nuclear pulses x (n); the digital nuclear signal processing module is used for processing the discrete negative index nuclear pulse x (n) to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to the terminal for display.
Further, the nuclear radiation signal acquisition module comprises a nuclear radiation detector, a preamplifier, a conditioning circuit unit and a high-speed analog-to-digital converter which are connected in sequence; the nuclear radiation detector is used for detecting nuclear radiation signals; the preamplifier is used for amplifying the nuclear radiation signal to obtain an amplified signal; the conditioning circuit unit is used for adjusting the amplified signal to obtain an adjustment signal; the high-speed analog-to-digital converter is used for carrying out digital processing on the adjustment signal to obtain discrete negative index nuclear pulse x (n).
Further, the digital core signal processing module includes an inverse RC unit, a delay-subtractor unit, a delay-adder unit, a first integrator, a second integrator and an adder, wherein an input end of the inverse RC unit is used as an input end of the digital core signal processing module, an output end of the inverse RC unit is respectively connected with an input end of the delay-subtractor unit and an input end of the delay-adder unit, an output end of the delay-subtractor unit is connected with an input end of the first integrator, an output end of the first integrator is connected with a first input end of the adder, an output end of the delay-adder unit is connected with a second input end of the adder, an output end of the adder is connected with an input end of the second integrator, and an output end of the second integrator is connected with a terminal.
The inverse RC unit is used for processing the discrete negative index nuclear pulse x (n) to obtain step pulse v (n); the delay-subtractor unit is used for processing the step pulse v (n) to obtain an inverse double rectangular pulse D1 (n); the delay-adder unit is used for processing the step pulse v (n) to obtain a forward double-step pulse D2 (n); the first integrator is used for processing the reverse double rectangular pulse D1 (n) to obtain a reverse double slope pulse P (n); the adder is used for summing the forward double-step pulse D2 (n) and the reverse double-slope pulse P (n) to obtain a symmetrical double-sawtooth pulse R (n); the second integrator is used for processing the symmetrical double-sawtooth pulse R (n) to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical double-sawtooth pulse S (n) to the terminal for display.
Further, the expressions of the step pulse v (n), the reverse double rectangular pulse D1 (n), the forward double step pulse D2 (n), the reverse double ramp pulse P (n), the symmetrical double saw tooth pulse R (n) and the symmetrical warhead-like pulse S (n) are respectively:
v(n)＝v(n-1)+x(n)-d*x(n-1)
D1(n)＝v(n-K-1)-v(n-1)+v(n-K-L)-v(n-L)
D2(n)＝(v(n)+v(n-K-L))*K
P(n)＝P(n-1)+D1(n)
R(n)＝P(n)+D2(n)
S(n)＝S(n-1)+R(n)
wherein x (·) represents a negative exponential kernel pulse function, v (·) represents a step pulse function, D1 (·) represents a reverse double rectangular pulse function, D2 (·) represents a forward double step pulse function, P (·) represents a reverse double ramp pulse function, R (·) represents a symmetric double saw tooth pulse function, S (·) represents a symmetric warhead-like pulse function, n represents a sampling point, D is a first exponent and d=exp (-Ts/τ), ts represents a sampling period of the high-speed analog-to-digital converter, τ represents an decay time constant, K represents a rise time of the symmetric warhead-like pulse, and L represents a sum of the rise time and the flat-top time of the symmetric warhead-like pulse.
The invention also provides a symmetrical warhead pulse forming method, which comprises the following steps:
s1, nuclear radiation signals are collected through a nuclear radiation signal collection module and are processed into discrete negative index nuclear pulses x (n).
S2, processing the discrete negative index nuclear pulse x (n) through a digital nuclear signal processing module to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to a terminal for display.
Further, step S1 includes the following sub-steps:
s11, detecting nuclear radiation signals through a nuclear radiation detector.
And S12, amplifying the nuclear radiation signal through a preamplifier to obtain an amplified signal.
S13, adjusting the amplified signal through the conditioning circuit unit to obtain an adjustment signal.
S14, performing digital processing on the adjusting signal through a high-speed analog-to-digital converter to obtain discrete negative index nuclear pulses x (n).
Further, step S2 includes the following sub-steps:
s21, processing the discrete negative index nuclear pulse x (n) through an inverse RC unit to obtain a step pulse v (n).
S22, processing the step pulse v (n) through a delay-subtractor unit to obtain an inverse double rectangular pulse D1 (n).
S23, processing the step pulse v (n) through a delay-adder unit to obtain a forward double-step pulse D2 (n).
S24, the reverse double rectangular pulse D1 (n) is processed through a first integrator, and a reverse double ramp pulse P (n) is obtained.
S25, summing the forward double step pulse D2 (n) and the reverse double slope pulse P (n) through an adder to obtain a symmetrical double sawtooth pulse R (n).
S26, processing the symmetrical double-sawtooth pulse R (n) through a second integrator to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to a terminal for display.
Further, the expressions of the step pulse v (n), the reverse double rectangular pulse D1 (n), the forward double step pulse D2 (n), the reverse double ramp pulse P (n), the symmetrical double saw tooth pulse R (n) and the symmetrical warhead-like pulse S (n) are respectively:
v(n)＝v(n-1)+x(n)-d*x(n-1)
D1(n)＝v(n-K-1)-v(n-1)+v(n-K-L)-v(n-L)
D2(n)＝(v(n)+v(n-K-L))*K
P(n)＝P(n-1)+D1(n)
R(n)＝P(n)+D2(n)
S(n)＝S(n-1)+R(n)
wherein x (·) represents a negative exponential kernel pulse function, v (·) represents a step pulse function, D1 (·) represents a reverse double rectangular pulse function, D2 (·) represents a forward double step pulse function, P (·) represents a reverse double ramp pulse function, R (·) represents a symmetric double saw tooth pulse function, S (·) represents a symmetric warhead-like pulse function, n represents a sampling point, D is a first exponent and d=exp (-Ts/τ), ts represents a sampling period of the high-speed analog-to-digital converter, τ represents an decay time constant, K represents a rise time of the symmetric warhead-like pulse, and L represents a sum of the rise time and the flat-top time of the symmetric warhead-like pulse.
The beneficial effects of the invention are as follows:
(1) The invention has simple structure and small operand, and is convenient to realize in the FPGA.
(2) The invention meets the technical requirements of energy resolution, pulse passing rate and the like, and has adjustable pulse forming parameters and strong self-adaptability.
(3) The invention introduces the flat-top time parameter, so that the flat-top parameter is adjustable, and when the flat-top duration is longer than the maximum charge collection time, the amplitude loss caused by ballistic loss can be effectively overcome, thereby accurately extracting the real amplitude of the original pulse.
(4) The invention provides a brand new digital nuclear pulse forming technology, which has initiatives.
Drawings
Fig. 1 is a block diagram of a symmetrical warhead pulse forming apparatus according to an embodiment of the present invention.
Fig. 2 is a diagram showing a symmetrical bullet pulse forming effect according to a first embodiment of the present invention.
Fig. 3 is a flowchart of a symmetrical warhead pulse forming method according to a second embodiment of the present invention.
Fig. 4 is a schematic diagram of pulse signals at each stage of a symmetrical warhead pulse forming method according to a second embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It is to be understood that the embodiments shown and described in the drawings are merely illustrative of the principles and spirit of the invention and are not intended to limit the scope of the invention.
Embodiment one:
the embodiment of the invention provides a symmetrical warhead pulse forming device, which is shown in fig. 1 and comprises a nuclear radiation signal acquisition module and a digital nuclear signal processing module, wherein the output end of the nuclear radiation signal acquisition module is connected with the input end of the digital nuclear signal processing module, and the output end of the digital nuclear signal processing module is connected with a terminal.
The nuclear radiation signal acquisition module is used for acquiring nuclear radiation signals and processing the nuclear radiation signals into discrete negative index nuclear pulses x (n); the digital nuclear signal processing module is used for processing the discrete negative index nuclear pulse x (n) to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to the terminal for display.
As shown in fig. 1, the nuclear radiation signal acquisition module comprises a nuclear radiation detector, a preamplifier, a conditioning circuit unit and a high-speed analog-to-digital converter which are connected in sequence; the nuclear radiation detector is used for detecting nuclear radiation signals; the preamplifier is used for amplifying the nuclear radiation signal to obtain an amplified signal; the conditioning circuit unit is used for adjusting the amplified signal to obtain an adjustment signal; the high-speed analog-to-digital converter is used for carrying out digital processing on the adjustment signal to obtain discrete negative index nuclear pulse x (n).
As shown in fig. 1, the digital core signal processing module includes an inverse RC unit, a delay-subtractor unit, a delay-adder unit, a first integrator, a second integrator, and an adder, where an input of the inverse RC unit is used as an input of the digital core signal processing module, an output of the inverse RC unit is connected to an input of the delay-subtractor unit and an input of the delay-adder unit, an output of the delay-subtractor unit is connected to an input of the first integrator, an output of the first integrator is connected to a first input of the adder, an output of the delay-adder unit is connected to a second input of the adder, an output of the adder is connected to an input of the second integrator, and an output of the second integrator is connected to a terminal.
The inverse RC unit is used for processing the discrete negative index nuclear pulse x (n) to obtain step pulse v (n); the delay-subtractor unit is used for processing the step pulse v (n) to obtain an inverse double rectangular pulse D1 (n); the delay-adder unit is used for processing the step pulse v (n) to obtain a forward double-step pulse D2 (n); the first integrator is used for processing the reverse double rectangular pulse D1 (n) to obtain a reverse double slope pulse P (n); the adder is used for summing the forward double-step pulse D2 (n) and the reverse double-slope pulse P (n) to obtain a symmetrical double-sawtooth pulse R (n); the second integrator is used for processing the symmetrical double-sawtooth pulse R (n) to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical double-sawtooth pulse S (n) to the terminal for display.
In the embodiment of the present invention, the step pulse v (n), the reverse double rectangular pulse D1 (n), the forward double step pulse D2 (n), the reverse double ramp pulse P (n), the symmetrical double saw tooth pulse R (n) and the symmetrical bullet-like pulse S (n) have the following expressions:
v(n)＝v(n-1)+x(n)-d*x(n-1)
D1(n)＝v(n-K-1)-v(n-1)+v(n-K-L)-v(n-L)
D2(n)＝(v(n)+v(n-K-L))*K
P(n)＝P(n-1)+D1(n)
R(n)＝P(n)+D2(n)
S(n)＝S(n-1)+R(n)
wherein x (·) represents a negative exponential kernel pulse function, v (·) represents a step pulse function, D1 (·) represents a reverse double rectangular pulse function, D2 (·) represents a forward double step pulse function, P (·) represents a reverse double ramp pulse function, R (·) represents a symmetric double saw tooth pulse function, S (·) represents a symmetric warhead-like pulse function, n represents a sampling point, D is a first exponent and d=exp (-Ts/τ), ts represents a sampling period of the high-speed analog-to-digital converter, τ represents an decay time constant, K represents a rise time of the symmetric warhead-like pulse, and L represents a sum of the rise time and the flat-top time of the symmetric warhead-like pulse.
In the embodiment of the present invention, the finally obtained symmetrical warhead-like pulse S (n) is shown in fig. 2, and as can be seen from fig. 2:
(1) The invention has adjustable forming parameters and strong self-adaptability.
(2) The invention can separate and accumulate pulses, accurately extract pulse amplitude information, and the forming method gives consideration to technical indexes such as energy resolution, pulse passing rate and the like.
(3) The invention introduces the flat-top time parameter, so that the flat-top parameter is adjustable, and when the flat-top duration is longer than the maximum charge collection time, the amplitude loss caused by ballistic loss can be effectively overcome, thereby accurately extracting the real amplitude of the original pulse.
Embodiment two:
the embodiment of the invention provides a symmetrical warhead pulse forming method, which is shown in fig. 3 and comprises the following steps S1-S2:
s1, nuclear radiation signals are collected through a nuclear radiation signal collection module and are processed into discrete negative index nuclear pulses x (n).
Step S1 includes the following sub-steps S11 to S14:
s11, detecting nuclear radiation signals through a nuclear radiation detector.
And S12, amplifying the nuclear radiation signal through a preamplifier to obtain an amplified signal.
S13, adjusting the amplified signal through the conditioning circuit unit to obtain an adjustment signal.
S14, performing digital processing on the adjusting signal through a high-speed analog-to-digital converter to obtain discrete negative index nuclear pulses x (n).
S2, processing the discrete negative index nuclear pulse x (n) through a digital nuclear signal processing module to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to a terminal for display.
As shown in fig. 4, step S2 includes the following substeps S21 to S26:
s21, processing the discrete negative index nuclear pulse x (n) through an inverse RC unit to obtain a step pulse v (n).
S22, processing the step pulse v (n) through a delay-subtractor unit to obtain an inverse double rectangular pulse D1 (n).
S23, processing the step pulse v (n) through a delay-adder unit to obtain a forward double-step pulse D2 (n).
S24, the reverse double rectangular pulse D1 (n) is processed through a first integrator, and a reverse double ramp pulse P (n) is obtained.
S25, summing the forward double step pulse D2 (n) and the reverse double slope pulse P (n) through an adder to obtain a symmetrical double sawtooth pulse R (n).
S26, processing the symmetrical double-sawtooth pulse R (n) through a second integrator to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to a terminal for display.
In the embodiment of the present invention, the step pulse v (n), the reverse double rectangular pulse D1 (n), the forward double step pulse D2 (n), the reverse double ramp pulse P (n), the symmetrical double saw tooth pulse R (n) and the symmetrical bullet-like pulse S (n) have the following expressions:
v(n)＝v(n-1)+x(n)-d*x(n-1)
D1(n)＝v(n-K-1)-v(n-1)+v(n-K-L)-v(n-L)
D2(n)＝(v(n)+v(n-K-L))*K
P(n)＝P(n-1)+D1(n)
R(n)＝P(n)+D2(n)
S(n)＝S(n-1)+R(n)
wherein x (·) represents a negative exponential kernel pulse function, v (·) represents a step pulse function, D1 (·) represents a reverse double rectangular pulse function, D2 (·) represents a forward double step pulse function, P (·) represents a reverse double ramp pulse function, R (·) represents a symmetric double saw tooth pulse function, S (·) represents a symmetric warhead-like pulse function, n represents a sampling point, D is a first exponent and d=exp (-Ts/τ), ts represents a sampling period of the high-speed analog-to-digital converter, τ represents an decay time constant, K represents a rise time of the symmetric warhead-like pulse, and L represents a sum of the rise time and the flat-top time of the symmetric warhead-like pulse.
According to the embodiment of the invention, the flat-top time parameter is introduced, so that the flat-top parameter is adjustable, and when the flat-top duration is longer than the maximum charge collection time, the amplitude loss caused by ballistic loss can be effectively overcome, thereby accurately extracting the real amplitude of the original pulse.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (4)
1. The symmetrical warhead pulse forming device is characterized by comprising a nuclear radiation signal acquisition module and a digital nuclear signal processing module, wherein the output end of the nuclear radiation signal acquisition module is connected with the input end of the digital nuclear signal processing module, and the output end of the digital nuclear signal processing module is connected with a terminal;
the nuclear radiation signal acquisition module is used for acquiring nuclear radiation signals and processing the nuclear radiation signals into discrete negative index nuclear pulses x (n);
the digital nuclear signal processing module is used for processing the discrete negative index nuclear pulse x (n) to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to the terminal for display;
the nuclear radiation signal acquisition module comprises a nuclear radiation detector, a preamplifier, a conditioning circuit unit and a high-speed analog-to-digital converter which are connected in sequence;
the nuclear radiation detector is used for detecting nuclear radiation signals;
the preamplifier is used for amplifying the nuclear radiation signal to obtain an amplified signal;
the conditioning circuit unit is used for adjusting the amplified signal to obtain an adjustment signal;
the high-speed analog-to-digital converter is used for carrying out digital processing on the adjustment signal to obtain discrete negative index nuclear pulse x (n);
the digital core signal processing module comprises an inverse RC unit, a delay-subtractor unit, a delay-adder unit, a first integrator, a second integrator and an adder, wherein the input end of the inverse RC unit is used as the input end of the digital core signal processing module, the output end of the inverse RC unit is respectively connected with the input end of the delay-subtractor unit and the input end of the delay-adder unit, the output end of the delay-subtractor unit is connected with the input end of the first integrator, the output end of the first integrator is connected with the first input end of the adder, the output end of the delay-adder unit is connected with the second input end of the adder, and the output end of the second integrator is connected with a terminal;
the inverse RC unit is used for processing the discrete negative index nuclear pulse x (n) to obtain step pulse v (n);
the delay-subtractor unit is used for processing the step pulse v (n) to obtain an inverse double rectangular pulse D1 (n);
the delay-adder unit is used for processing the step pulse v (n) to obtain a forward double-step pulse D2 (n);
the first integrator is used for processing the reverse double rectangular pulse D1 (n) to obtain a reverse double slope pulse P (n);
the adder is used for summing the forward double-step pulse D2 (n) and the reverse double-slope pulse P (n) to obtain a symmetrical double-sawtooth pulse R (n);
the second integrator is used for processing the symmetrical double-sawtooth pulse R (n) to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical double-sawtooth pulse S (n) to the terminal for display.
2. The symmetrical warhead-like pulse shaping apparatus of claim 1, wherein the step pulse v (n), the inverted double rectangular pulse D1 (n), the forward double step pulse D2 (n), the inverted double ramp pulse P (n), the symmetrical double saw tooth pulse R (n) and the symmetrical warhead-like pulse S (n) are expressed by:
v(n)＝v(n-1)+x(n)-d*x(n-1)
D1(n)＝v(n-K-1)-v(n-1)+v(n-K-L)-v(n-L)
D2(n)＝(v(n)+v(n-K-L))*K
P(n)＝P(n-1)+D1(n)
R(n)＝P(n)+D2(n)
S(n)＝S(n-1)+R(n)
wherein x (·) represents a negative exponential kernel pulse function, v (·) represents a step pulse function, D1 (·) represents a reverse double rectangular pulse function, D2 (·) represents a forward double step pulse function, P (·) represents a reverse double ramp pulse function, R (·) represents a symmetric double saw tooth pulse function, S (·) represents a symmetric warhead-like pulse function, n represents a sampling point, D is a first exponent and d=exp (-Ts/τ), ts represents a sampling period of the high-speed analog-to-digital converter, τ represents an decay time constant, K represents a rise time of the symmetric warhead-like pulse, and L represents a sum of the rise time and the flat-top time of the symmetric warhead-like pulse.
3. A symmetrical warhead-like pulse forming method, comprising the steps of:
s1, collecting nuclear radiation signals through a nuclear radiation signal collecting module, and processing the nuclear radiation signals into discrete negative index nuclear pulses x (n);
s2, processing the discrete negative index nuclear pulse x (n) through a digital nuclear signal processing module to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to a terminal for display;
the step S1 comprises the following sub-steps:
s11, detecting nuclear radiation signals through a nuclear radiation detector;
s12, amplifying the nuclear radiation signal through a preamplifier to obtain an amplified signal;
s13, adjusting the amplified signal through a conditioning circuit unit to obtain an adjustment signal;
s14, performing digital processing on the adjustment signal through a high-speed analog-to-digital converter to obtain discrete negative index nuclear pulses x (n);
the step S2 comprises the following sub-steps:
s21, processing discrete negative index nuclear pulses x (n) through an inverse RC unit to obtain step pulses v (n);
s22, processing the step pulse v (n) through a delay-subtractor unit to obtain a reverse double rectangular pulse D1 (n);
s23, processing the step pulse v (n) through a delay-adder unit to obtain a forward double-step pulse D2 (n);
s24, processing the reverse double rectangular pulse D1 (n) through a first integrator to obtain a reverse double ramp pulse P (n);
s25, summing the forward double step pulse D2 (n) and the reverse double slope pulse P (n) through an adder to obtain a symmetrical double sawtooth pulse R (n);
s26, processing the symmetrical double-sawtooth pulse R (n) through a second integrator to obtain symmetrical warhead-like pulse S (n), and transmitting the symmetrical warhead-like pulse S (n) to a terminal for display.
4. A symmetrical warhead-like pulse shaping method as claimed in claim 3, wherein the expressions of the step pulse v (n), the inverse double rectangular pulse D1 (n), the forward double step pulse D2 (n), the inverse double ramp pulse P (n), the symmetrical double saw tooth pulse R (n) and the symmetrical warhead-like pulse S (n) are respectively:
v(n)＝v(n-1)+x(n)-d*x(n-1)
D1(n)＝v(n-K-1)-v(n-1)+v(n-K-L)-v(n-L)
D2(n)＝(v(n)+v(n-K-L))*K
P(n)＝P(n-1)+D1(n)
R(n)＝P(n)+D2(n)
S(n)＝S(n-1)+R(n)
wherein x (·) represents a negative exponential kernel pulse function, v (·) represents a step pulse function, D1 (·) represents a reverse double rectangular pulse function, D2 (·) represents a forward double step pulse function, P (·) represents a reverse double ramp pulse function, R (·) represents a symmetric double saw tooth pulse function, S (·) represents a symmetric warhead-like pulse function, n represents a sampling point, D is a first exponent and d=exp (-Ts/τ), ts represents a sampling period of the high-speed analog-to-digital converter, τ represents an decay time constant, K represents a rise time of the symmetric warhead-like pulse, and L represents a sum of the rise time and the flat-top time of the symmetric warhead-like pulse.
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